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2. Consider the so-called Pauli operators ôx = [0)(1| + |1) (0], ôy = −i|0)(1| +i|1)(0] and O₂ = 0) (011) [1], where {10), 11)} form an orthonormal basis of the considered Hilbert space. (a) Show that each Pauli operator is Hermitian. (b) Write down the matrix representation of the Pauli operators. Hint: for an operator A and an orthonormal basis {løk)}k, the matrix element Ajk is defined as (pj|A|øk).

2. Consider the so-called Pauli operators ôx = [0)(1| + |1) (0], ôy = −i|0)(1| +i|1)(0] and O₂ = 0) (011) [1], where {10), 11)} form an orthonormal basis of the considered Hilbert space. (a) Show that each Pauli operator is Hermitian. (b) Write down the matrix representation of the Pauli operators. Hint: for an operator A and an orthonormal basis {løk)}k, the matrix element Ajk is defined as (pj|A|øk).

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2. Consider the so-called Pauli operators ôx = [0)(1| + |1)(0], ôy = −i|0)(1| + i|1) (0] and ôz = 0) (0 - 1)(1), where {10), 11)} form an orthonormal basis of the considered Hilbert space. (a) Show that each Pauli operator is Hermitian. (b) Write down the matrix representation of the Pauli operators. Hint: for an operator  and an orthonormal basis {lok)}k, the matrix element Ajk is defined as (pj|Â|øk).
Transcribed Image Text:2. Consider the so-called Pauli operators ôx = [0)(1| + |1)(0], ôy = −i|0)(1| + i|1) (0] and ôz = 0) (0 - 1)(1), where {10), 11)} form an orthonormal basis of the considered Hilbert space. (a) Show that each Pauli operator is Hermitian. (b) Write down the matrix representation of the Pauli operators. Hint: for an operator  and an orthonormal basis {lok)}k, the matrix element Ajk is defined as (pj|Â|øk).
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